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Author: Tinku Tara

Question-149400

Question Number 149400 by mathdanisur last updated on 05/Aug/21 Answered by liberty last updated on 05/Aug/21 $$\mathrm{let}\:\mathrm{tan}\:\mathrm{2}=\mathrm{x}\:\begin{cases}{\mathrm{sin}\:\mathrm{2}=\frac{\mathrm{x}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}}}\\{\mathrm{cos}\:\mathrm{2}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}}}\end{cases} \\ $$$$\mathrm{let}\:\mathrm{cos}\:\mathrm{6}=\mathrm{y}\Rightarrow\mathrm{2cos}\:^{\mathrm{2}} \mathrm{3}−\mathrm{1}=\mathrm{y} \\ $$$$\mathrm{cos}\:\mathrm{3}=\sqrt{\frac{\mathrm{y}+\mathrm{1}}{\mathrm{2}}}\:\wedge\:\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}} \mathrm{3}=\mathrm{y}…

what-Maclaurin-series-of-function-tan-x-

Question Number 83864 by jagoll last updated on 07/Mar/20 $$\mathrm{what}\:\mathrm{Maclaurin}\:\mathrm{series}\:\mathrm{of}\:\mathrm{function} \\ $$$$\mathrm{tan}\:\left(\mathrm{x}\right)? \\ $$ Commented by niroj last updated on 07/Mar/20 $$\:\mathrm{Solution}: \\ $$$$\:\:\mathrm{let},\:\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{tan}\:\mathrm{x}\:\:,\:\:\mathrm{f}_{\mathrm{0}} \left(\mathrm{0}\right)=\mathrm{0}…

lim-x-x-2x-2-x-2x-3-

Question Number 83865 by jagoll last updated on 07/Mar/20 $$\underset{{x}\rightarrow−\infty\:} {\mathrm{lim}}\:\left(\mathrm{x}\sqrt{\mathrm{2x}+\mathrm{2}}−\mathrm{x}\sqrt{\mathrm{2x}+\mathrm{3}}\right) \\ $$ Commented by mr W last updated on 07/Mar/20 $$\mathrm{2}{x}+\mathrm{2}\geqslant\mathrm{0} \\ $$$$\Rightarrow{x}\geqslant−\mathrm{1} \\…

An-object-of-mass-7kg-is-sliding-down-a-frictionless-20m-inclined-plane-Calculate-the-speed-of-the-object-when-it-reaches-the-ground-

Question Number 83861 by Umar last updated on 07/Mar/20 $$\mathrm{An}\:\mathrm{object}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{7kg}\:\mathrm{is}\:\mathrm{sliding}\:\mathrm{down} \\ $$$$\mathrm{a}\:\mathrm{frictionless}\:\mathrm{20m}\:\mathrm{inclined}\:\mathrm{plane}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{object}\:\mathrm{when}\: \\ $$$$\mathrm{it}\:\mathrm{reaches}\:\mathrm{the}\:\mathrm{ground}. \\ $$ Commented by mr W last updated on…

The-pulley-arrangements-are-identical-The-mass-of-the-rope-is-negligible-In-a-the-mass-m-is-lifted-up-by-attaching-a-mass-2m-to-the-other-end-of-the-rope-In-b-m-is-lifted-up-by-pulling-the-

Question Number 18322 by Tinkutara last updated on 18/Jul/17 $$\mathrm{The}\:\mathrm{pulley}\:\mathrm{arrangements}\:\mathrm{are}\:\mathrm{identical}. \\ $$$$\mathrm{The}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rope}\:\mathrm{is}\:\mathrm{negligible}.\:\mathrm{In} \\ $$$$\left(\mathrm{a}\right),\:\mathrm{the}\:\mathrm{mass}\:{m}\:\mathrm{is}\:\mathrm{lifted}\:\mathrm{up}\:\mathrm{by}\:\mathrm{attaching} \\ $$$$\mathrm{a}\:\mathrm{mass}\:\left(\mathrm{2}{m}\right)\:\mathrm{to}\:\mathrm{the}\:\mathrm{other}\:\mathrm{end}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rope}. \\ $$$$\mathrm{In}\:\left(\mathrm{b}\right),\:{m}\:\mathrm{is}\:\mathrm{lifted}\:\mathrm{up}\:\mathrm{by}\:\mathrm{pulling}\:\mathrm{the} \\ $$$$\mathrm{other}\:\mathrm{end}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rope}\:\mathrm{with}\:\mathrm{a}\:\mathrm{constant} \\ $$$$\mathrm{downward}\:\mathrm{force}\:{F}\:=\:\mathrm{2}{mg}.\:\mathrm{In}\:\mathrm{which} \\ $$$$\mathrm{case},\:\mathrm{the}\:\mathrm{acceleration}\:\mathrm{of}\:{m}\:\mathrm{is}\:\mathrm{more}? \\…

Question-149395

Question Number 149395 by mathdanisur last updated on 05/Aug/21 Answered by Olaf_Thorendsen last updated on 05/Aug/21 $$\int_{{a}} ^{{b}} {f}\left({x}\right)\:{dx}\:=\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{b}−{a}}{{n}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{f}\left({a}+{k}\frac{{b}−{a}}{{n}}\right) \\ $$$$\int_{\mathrm{3}} ^{\mathrm{5}}…